Network models and digital technologies in advanced training of mathematics teachers

The research problem and the rationale for its relevance. A teacher in today's environment is a teacher, a guide to the world of science, an innovator, and a role model. During the era of digital transformation of education, the demands on the teacher are increasing manifold. Therefore, teachers need to constantly develop their capabilities and professionalism. The relevance of the study is determined by the improvement of the modern educational process (introduction of innovative programs, digital platforms, etc.), which undoubtedly requires special attention to the improvement of teachers' competencies. The goal of the research is to substantiation and description of the use of network models and digital technologies in the system of advanced training of teachers for the effective formation of individual trajectories for improving the professionalism of a mathematics teacher. Methodology. The methodological basis of the study is the ideas of the subject-activity approach, including the subject-environment approach, which are used to form a network professional environment aimed at continuous improvement of the skills of teachers and the formation of individual teacher development trajectories. Results. The advanced training system is a complex multifaceted area. The study considers one of the options for modeling a system of continuous improvement of subject competencies of a mathematics teacher or a teacher in the system of additional mathematical education. The implementation of the proposed model for the formation of individual trajectories for improving the subject competencies of a teacher is analyzed.